Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | #338⋊C9 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10588302 |
| commutator, cosocle, hypocenter | #338⋊C9 | C2 |
| Frattini | C22×C3×C4 | S4 |
| Fitting | C3×#338 | D3 |
| socle | C2×C3 | #4622 |
| hypercenter | C4 | #63419 |
| LCS | G ▷ #338⋊C9 | |
| UCS | C1 ◁ C2 ◁ C4 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2,3^2,2^6|b^3=c,d^2=f,e^2=fgh,f^2=i,b^a=b^2c^2,c^a=c^2,d^a=deghi,e^a=efg,f^a=fhi,g^a=gh,d^b=eghi,e^b=def,f^b=fghi,g^b=hi,h^b=ghi,e^d=efg,h^d=hi,f^e=fi,g^e=gi36 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153933);